Problem: What do the following two equations represent? $2x-3y = 3$ $9x+6y = -5$
Putting the first equation in $y = mx + b$ form gives: $2x-3y = 3$ $-3y = -2x+3$ $y = \dfrac{2}{3}x - 1$ Putting the second equation in $y = mx + b$ form gives: $9x+6y = -5$ $6y = -9x-5$ $y = -\dfrac{3}{2}x - \dfrac{5}{6}$ The slopes are negative inverses of each other, so the lines are perpendicular.